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There are a lot of uncertainties in the water resources system, which makes the water allocation plan very risky. In order to analyze the risks of water resources allocation under uncertain conditions, a new methodology called the stochastic simulation-based risk assessment approach is developed in this paper. First, the main hydrological stochastic variable is fitted by a proper probability distribution. Second, suitable two-stage stochastic programming is constructed to obtain the expected benefit and optimized water allocation targets. Third, the Monte Carlo method is used to obtain a suitable stochastic sample of the hydrological variable. Fourth, a pre-allocated water optimization model is proposed to obtain optimized actual benefit. The methodology can give a way for risk analysis of water allocation plans obtained by uncertain optimization models, which provides reliable assistance to water managers in decision-making. The proposed methodology is applied to the Zhanghe Irrigation District and the risk of the water allocation plan obtained under the randomness of annual inflow is assessed. In addition, three different division methods of the annual inflow are applied in the first step, namely three levels, five levels and seven levels, respectively. From the results, the risk of the water allocation scheme obtained by the TSP model is 0.372–0.411 and decreases with the increase of the number of hydrological levels. Considering both the risk and model complexity, seven hydrological levels are recommended when using the TSP model to optimize water allocation under stochastic uncertainty.

In regional water management, various uncertainties such as randomness, non-stationarities, dynamics and complexities, lead to difficulties for water managers. To deal with the above problems, a new methodology is proposed by introducing two methods nonstationary analysis, where the generalized additive model is selected to analyze and fit the distribution of water inflow; and model optimization, where an interval multistage water classified-allocation model (IMWCA) is formulated to optimally allocate the available water. By incorporating multistage stochastic programming, interval parameter programming and classification thought, the IMWCA model can tackle both stochastic and imprecise uncertainties, realize inter-seasonal dynamic allocation, and address the complexity of various water users. The methodology is applied to the Zhanghe Irrigation District to optimize water allocation for municipality, industry, hydropower and agriculture among winter, spring, summer and autumn. The Zhanghe Reservoir seasonal inflow is found to be nonstationary for all the seasons and can be well fitted by the corresponding distributions, showing the sense of nonstationary analysis. Additionally, the comparison with the other model demonstrates the need for classification. From the results, municipality and industry are more competitive than hydropower. The Dongbao, Dangyang and Zhanghe districts have a higher priority than the Jingzhou and Shayang districts for irrigation water. Water requirements are more likely to be satisfied in autumn. These solutions of optimal targets and optimal water allocation are valuable for optimizing inter- and intra-seasonal water resource allocation under uncertainty.

Due to climate change and human activities, the assumption of the stationarity of hydrological variables will no longer hold. Moreover, the stochastic uncertainty of hydrological variables ...

Seasonal drought has become an important factor in agricultural production in humid and semi-humid areas. In this study, to mitigate the impact of seasonal drought, a new integrated mathematical model is proposed for optimal multi-crop irrigation scheduling, which is associated with conjunctive operation of reservoirs and ponds to maximize the annual returns for a reservoir-pond irrigation system. This objective is achieved via the use of two models: an operating policy model, which considers the regulatory role of ponds and optimizes reservoirs and ponds releases in one third of a month, and an allocation model, which optimizes irrigation allocations across crops by addressing water production function. The uneven distribution of ponds is also considered by dividing the irrigation district into many sub-districts. Artificial bee colony algorithm is innovatively improved by incorporating differential evolution algorithm and particle swarm optimization algorithm to solve this nonlinear, high-dimensional and complex optimization problem. The methodology is applied to the Zhanghe Irrigation Distict, which is located in Hubei Province of China, to demonstrate its applicability, and three additional models are simulated to demonstrate the validity of the integrated model. The results indicate that the integrated model can alleviate the impact of the seasonal drought and has remarkable optimization effect, especially for drought years. The average annual return calculated by the integrated model is 7.9, 7.0 and 3.1 % higher than that of the remaining three models, respectively. And in the special dry year, in which the frequency of rainfall is 95 %, the annual return calculated by the integrated model is 24.5, 21.8 and 10.1 % higher than that of the remaining three models, respectively.